Derivações localmente nilpotentes e os teoremas de Rentschler e Jung

• Autor(a) principal: Abreu, Kelyane Barboza de
• Data de Publicação: 2014
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UFPB
• Texto Completo: https://repositorio.ufpb.br/jspui/handle/tede/7438
• topic: Derivações localmente nilpotentes; Teorema de Rentschler; Teorema de Jung; Locally nilpotent derivations; Rentschler s theorem; Jung s theorem; CIENCIAS EXATAS E DA TERRA::MATEMATICA

The main goal of this work is to furnish a proof of the well-known Rentschler s Theorem, which describes the structure of the locally nilpotent derivations on the polynomial ring in two indeterminates (over a field of characteristic zero), up to conjugation by tame automorphisms. As a central application of this result, we prove Jung s Theorem, concerning the generators of the group of automorphisms in two variables. Finally, some examples are discussed, illustrating connections to other important topics.